In a large bowl, combine ground turkey, garlic, and parsley. Shape meat into 6 hamburger patties and season outside of each patty generously with salt and pepper.
Grill hamburgers on medium-high heat, turning once until hamburgers register 165F, about 10-13 minutes. Keep hamburgers warm and set aside a moment.
Grill the tomatoes: Brush tomato slices with olive oil and season with salt and pepper. Grill tomatoes over medium-high heat, turning once until slices have grill marks and are slightly softened. Set aside.
Place hamburgers on a sheet pan and top with mozzarella slices. Broil on high heat 1-2 minutes or until cheese is bubbly and golden.
Place hamburger patties on hamburger buns and top each patty with basil pesto, and grilled tomatoes. Replace bun tops and serve hamburgers immediately while warm. Enjoy!